Question

The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a player at third base, what is the distance the player has to throw?

Answer 1

well the question doesnt show any number for a side or anything but we can solve this with algebra if we say that a side from one base to next has a length of x. so we know each side has length x and that the shape they make is square. This means we are only searching for the diagonal of a square.

remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using the pythagoream theorem we can say that
a^2 + b^2 = c^2

we said all side lengths are x so we can put x in for a and b and get

x^2 + x^2 = c^2

2x^2 = c^2

c = x * squareroot(2)

that is the basic fundamental answer that will always work when working with diagonals of squares.

so if the length between bases is 90 ft, we could plug this in and get
c = 90 ft * squareroot(2)
c = 127.28 ft

Answer 2

In baseball field bounded by home plate, first, second, and third base is a square, distance of throw from first to third base is a²√2 units.

What is area of square?

Area of square is the square of its side length. It can be given as,

$A=a^2$

Here, (a) is the length of the side of the square

It is given that, the area of a baseball field bounded by home plate, first base, second base, and third base is a square.

Player at first base throws the ball to a player at third base.

The image of the baseball field is shown below.

As the area of a baseball field bounded by home plate, first base, second base, and third base is a square.

Thus the distance of player at first base throws the ball to a player at third base is the diagonal of this square.

Suppose the distance of the side of the baseball field is a meters. Thus The length of the diagonal of the square can be given as,

x=a²√2

Thus, In the baseball field bounded by home plate, first base, second base, and third base is a square, the  distance the player has to throw is a²√2 units when side is a units..

Learn more about the area of square here;

https://brainly.com/question/1658516